{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "nalgebra是一个Rust库，用于线性代数和数值计算。它提供了多种数据结构和算法，用于处理矩阵、向量、线性方程、最小二乘问题等。 \n",
    "\n",
    "https://nalgebra.org/docs/user_guide/points_and_transformations\n",
    "# 旋转和平移"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    ":dep nalgebra = \"0.33.0\" # 引入第三方依赖\n",
    ":dep approx = \"0.5.0\" # 引入第三方依赖\n",
    "\n",
    "use nalgebra as na;\n",
    "use na::{Isometry2, Point2, Vector2, Point3, Vector3, Vector4, Matrix4, Translation3};\n",
    "use approx::assert_relative_eq;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "+ 点a与向量v的和得到另一个点，该点是向量v对a的平移\n",
    "+  两个点b和a的差返回向量v,b = a + v;\n",
    "+  两点的和、乘、除是无意义的，不被nalgebra代数支持\n",
    "+  为方便起见，您可以使用自由函数 na::center(a, b) 计算两点的中心\n",
    "+  点的齐次坐标通常以 1 结束，而矢量的齐次坐标总是以 0 结束。\n",
    "+  点受变换的平移分量影响，而向量仅旋转和缩放"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "旋转后平移 t * p:{0, 0.99999994}\n",
      "旋转后平移 v: \n",
      "  ┌   ┐\n",
      "  │ 1 │\n",
      "  │ 0 │\n",
      "  └   ┘\n",
      "\n",
      " t * v:\n",
      "  ┌                   ┐\n",
      "  │                -1 │\n",
      "  │ -0.00000008742278 │\n",
      "  └                   ┘\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "let t = Isometry2::new(Vector2::new(1.0, 1.0), std::f32::consts::PI); // 绕点(0,0) 旋转π弧度，然后平移(1,1)\n",
    "let p = Point2::new(1.0, 0.0); // 受到旋转和平移的影响\n",
    "let v = Vector2::x();          // X轴的方向向量，受到旋转的影响，而不受到平移的影响\n",
    "\n",
    "//绕点(0,0) 旋转π弧度， 得到 (-1, 0), //然后平移(1,1), 得到 (-1+1, 0+1) = (0, 1)\n",
    "let p_t = t * p;\n",
    "println!(\"旋转后平移 t * p:{}\", p_t);\n",
    "\n",
    "let v_t = t * v;\n",
    "println!(\"旋转后平移 v: {} t * v:{}\", v, v_t);\n",
    "// assert_relative_eq!(t * v, Vector2::new(-1.0, 0.0));\n",
    "// //                                      ^^^^^\n",
    "// //                                   rotated only\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "构建点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "let p0 = Point3::new(2.0, 3.0, 4.0);\n",
    "\n",
    "// 从坐标向量建立\n",
    "let coords = Vector3::new(2.0, 3.0, 4.0);\n",
    "let p1 = Point3::from_coordinates(coords);\n",
    "\n",
    "// 从原点和坐标向量建立\n",
    "let translation = Vector3::new(2.0, 3.0, 4.0);\n",
    "let p2 = Point3::origin() + translation;\n",
    "\n",
    "let homogeneous_coords = Vector4::new(20.0, 30.0, 40.0, 10.0);\n",
    "let p3 = Point3::from_homogeneous(homogeneous_coords);\n",
    "\n",
    "assert_eq!(p0, p1);\n",
    "assert_eq!(p0, p2);\n",
    "assert_eq!(p0, p3.unwrap());"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 转换\n",
    "变换是作用于点和向量以改变其坐标的代数实体。下图显示了nalgebra上专用类型支持的所有转换（像 Affine2/3 这样的符号表示 Affine2 或 Affine3 ）：\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "此图中显示的所有类型实际上都是泛型类型wrt的类型别名。尺寸，并且名称以 Base 而不是数字结尾，即，翻译的基本实现是 TranslationBase 。更通用的转换 Transform2/3 、 Projective2/3 和 Affine2/3 是参数化类型 TransformBase<..., Category> 的别名，其中其最后一个类型参数 Category 指定表示三个变体中的哪一个。注意，原始矩阵也可以被解释为不一定可逆的一般变换。这在一般上下文中可能是有用的。\n",
    "\n",
    "转换可以组合（通过乘法），即使它们不具有相同的类型。合成结果的类型是两者的最一般变换。例如，将 Projective3 （可逆变换）与 Similarity3 相乘会产生 Projective3 ，因为所有相似性都是可逆的。一个例外是任何纯旋转与纯平移的乘积：没有一个比另一个更一般，所以结果是 Isometry2/3 ，这是足以表示这种组合的最具体的变换。\n",
    "\n",
    "使用 na::convert(...) 函数可以将转换转换为更通用的转换。反过来，有时也可以使用 na::try_convert(...) ，它在成功的情况下返回一个非 None 值。例如，只有当相似性缩放因子为1时（由 ::try_convert(...) 在运行时检查），将 Similarity2 转换为 Isometry2 才会成功。请注意，如果您不想在转换时消耗输入值，请使用带引用的 na::convert_ref(...) 和 na::try_convert_ref(...) 。"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    },
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 与点的交互\n",
    "\n",
    "人们自然会想知道，在齐次坐标中表示的变换如何应用于向量和点。例如，将 Vector2 乘以 Rotation2 将产生旋转的 Vector2 。另一方面，将 Vector2 乘以 Matrix3 （通过将2D旋转转换为齐次坐标获得）甚至无法编译！唯一的解决方案是以某种方式将2D向量转换为 Vector3 并执行乘法。同样的推理也适用于点：我们需要将 Point2 转换为 Vector3 。这些转换可以通过使用 .to_homogeneous() 计算向量和点本身的齐次坐标来完成。\n",
    "\n",
    "计算向量的齐次坐标将附加 0 ，而计算点的齐次坐标将附加 1 ：\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "这种微妙的区别反映了本章开头强调的事实：变换对点的影响不同于对向量的影响。附加到矢量的 0 将消除任何变换的平移分量;附加到点的 1 将使其正常平移。\n",
    "\n",
    "齐次坐标中的点和向量可以使用 ::from_homogeneous(...) 转换回来。对于矢量，最后一个坐标条目将被删除。对于点，最后一个坐标也将被删除，每隔一个坐标将被它除：\n",
    "![image-2.png](attachment:image-2.png)\n",
    "\n",
    "下面的示例显示了使用两种方法应用变换：专用变换类型和齐次坐标。虽然最终结果是相同的，但使用专用类型更简洁和有效。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "// With dedicated transform types.\n",
    "let iso = Isometry2::new(Vector2::new(1.0, 1.0), std::f32::consts::PI);\n",
    "let pt  = Point2::new(1.0, 0.0);\n",
    "let vec = Vector2::x();\n",
    "\n",
    "let transformed_pt  = iso * pt;\n",
    "let transformed_vec = iso * vec;\n",
    "\n",
    "assert_relative_eq!(transformed_pt, Point2::new(0.0, 1.0));\n",
    "assert_relative_eq!(transformed_vec, Vector2::new(-1.0, 0.0));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "Error",
     "evalue": "Couldn't automatically determine type of variable `hom_iso`.\nPlease give it an explicit type.",
     "output_type": "error",
     "traceback": [
      "Couldn't automatically determine type of variable `hom_iso`.\nPlease give it an explicit type."
     ]
    }
   ],
   "source": [
    "// 等距转换矩阵\n",
    "let iso = Isometry2::new(Vector2::new(1.0, 1.0), std::f32::consts::PI);\n",
    "let pt  = Point2::new(1.0, 0.0);\n",
    "let vec = Vector2::x();\n",
    "\n",
    "// 计算齐次坐标系\n",
    "let hom_iso = iso.to_homogeneous();\n",
    "let hom_pt  = pt.to_homogeneous();  //齐次坐标点\n",
    "let hom_vec = vec.to_homogeneous();\n",
    "\n",
    "let hom_transformed_pt  = hom_iso * hom_pt;\n",
    "let hom_transformed_vec = hom_iso * hom_vec; //平移没有影响\n",
    "\n",
    "// Convert back to the cartesian coordinates.\n",
    "let transformed_pt  = Point2::from_homogeneous(hom_transformed_pt).unwrap();\n",
    "let transformed_vec = Vector2::from_homogeneous(hom_transformed_vec).unwrap();\n",
    "\n",
    "assert_relative_eq!(transformed_pt, Point2::new(0.0, 1.0));\n",
    "assert_relative_eq!(transformed_vec, Vector2::new(-1.0, 0.0));"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Projections 投影\n",
    "代数中的投影是计算机图形学界通常定义的投影。尤其是，它们并不像有些人习惯的那样是幂等的。相反，它们是双射映射，将给定的六面凸形变换为以原点为中心的双单位立方体（即轴对齐立方体，由坐标为\n",
    "(-1,-1,-1)到(1,1,1). 得到的坐标通常被计算机制图界称为归一化设备坐标（对应于剪辑空间）：\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "本节介绍如何执行计算机图形（CG）的一些常见操作。请注意，虽然3D计算机图形社区几乎只使用4×4矩阵，但nalgebra定义了更广泛的转换类型，强烈建议用户使用这些类型。\n",
    "\n",
    "创建后，可以通过附加或前置转换来修改 Matrix4 （或2D转换的 Matrix3 ）。函数签名遵循与上面列出的转换矩阵创建函数相同的模式。支持就地追加和前置，并具有带 _mut 后缀的名称，例如， .append_scaling_mut(...) 而不是 .append_scaling(...) 。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m = \n",
      "  ┌         ┐\n",
      "  │ 2 0 0 0 │\n",
      "  │ 0 2 0 0 │\n",
      "  │ 0 0 2 0 │\n",
      "  │ 0 0 0 1 │\n",
      "  └         ┘\n",
      "\n",
      "\n",
      "Vector3::x() = [[2.0, 0.0, 0.0]]\n",
      "m.append_nonuniform_scaling_mut = \n",
      "  ┌         ┐\n",
      "  │ 2 0 0 0 │\n",
      "  │ 0 4 0 0 │\n",
      "  │ 0 0 6 0 │\n",
      "  │ 0 0 0 1 │\n",
      "  └         ┘\n",
      "\n",
      "\n",
      "m.append_translation = \n",
      "  ┌             ┐\n",
      "  │  2  0  0 42 │\n",
      "  │  0  4  0  0 │\n",
      "  │  0  0  6  0 │\n",
      "  │  0  0  0  1 │\n",
      "  └             ┘\n",
      "\n",
      "\n",
      "变换矩阵间的左乘和右乘\n",
      "\n",
      "m: \n",
      "  ┌         ┐\n",
      "  │ 2 0 0 0 │\n",
      "  │ 0 4 0 0 │\n",
      "  │ 0 0 6 0 │\n",
      "  │ 0 0 0 1 │\n",
      "  └         ┘\n",
      "\n",
      "\n",
      "rot: \n",
      "  ┌                                                                                             ┐\n",
      "  │                      1                      0                      0                      0 │\n",
      "  │                      0    -0.9999987317275395 -0.0015926529164868282                      0 │\n",
      "  │                      0  0.0015926529164868282    -0.9999987317275395                      0 │\n",
      "  │                      0                      0                      0                      1 │\n",
      "  └                                                                                             ┘\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "// 创建缩放因子为 2 的统一缩放矩阵。\n",
    "let mut m =  Matrix4::new_scaling(2.0);\n",
    "println!(\"m = {}\", m);\n",
    "println!(\"Vector3::x() = {:?}\", Vector3::x() * 2.0);\n",
    "\n",
    "assert_eq!(m.transform_vector(&Vector3::x()), Vector3::x() * 2.0); //[[2.0, 0.0, 0.0]]\n",
    "assert_eq!(m.transform_vector(&Vector3::y()), Vector3::y() * 2.0);\n",
    "assert_eq!(m.transform_vector(&Vector3::z()), Vector3::z() * 2.0);\n",
    "\n",
    "// 就地添加非均匀缩放。\n",
    "m.append_nonuniform_scaling_mut(&Vector3::new(1.0, 2.0, 3.0));\n",
    "println!(\"m.append_nonuniform_scaling_mut = {}\", m); \n",
    "\n",
    "assert_eq!(m.transform_vector(&Vector3::x()), Vector3::x() * 2.0);\n",
    "assert_eq!(m.transform_vector(&Vector3::y()), Vector3::y() * 4.0);\n",
    "assert_eq!(m.transform_vector(&Vector3::z()), Vector3::z() * 6.0);\n",
    "\n",
    "// 在前面变换的基础上，平移42个单位\n",
    "let m2 = m.append_translation(&Vector3::new(42.0, 0.0, 0.0));\n",
    "println!(\"m.append_translation = {}\", m2);\n",
    "//相当于对应的轴数值放大后，叠加平移\n",
    "assert_eq!(m2.transform_point(&Point3::new(1.0, 1.0, 1.0)), Point3::new(42.0 + 2.0, 4.0, 6.0));\n",
    "\n",
    "// 创建旋转矩阵\n",
    "let rot        = Matrix4::from_scaled_axis(&Vector3::x() * 3.14);\n",
    "println!(\"变换矩阵间的左乘和右乘\\n\");\n",
    "println!(\"m: {}\", m);\n",
    "println!(\"rot: {}\", rot);\n",
    "let rot_then_m = m * rot; // 右乘法等同于在 `m` 前加上 `rot`\n",
    "let m_then_rot = rot * m; // 左乘法等同于将 `rot` 追加到 `m`。\n",
    "\n",
    "let pt = Point3::new(1.0, 2.0, 3.0);\n",
    "\n",
    "assert_relative_eq!(m.transform_point(&rot.transform_point(&pt)), rot_then_m.transform_point(&pt));\n",
    "assert_relative_eq!(rot.transform_point(&m.transform_point(&pt)), m_then_rot.transform_point(&pt));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对点和向量使用原始变换矩阵#\n",
    "\n",
    "Use the .transform_vector(...) and .transform_point(...) methods that directly take a Vector3 and Point3 as argument.\n",
    "使用 .transform_vector(...) 和 .transform_point(...) 方法，直接将 Vector3 和 Point3 作为参数。\n",
    "\n",
    "向量和点也使用齐次坐标。在这种情况下，3D矢量 Vector3::new(x, y, z) 应该被给定为第四坐标设置为零，即 Vector4::new(x, y, z, 0.0) ，而3D点 Point3::new(x, y, z) 应该被表示为其第四坐标等于1的矢量，即，三号。然后 Matrix4 可以直接乘以增广向量。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "let mut m = Matrix4::new_rotation_wrt_point(Vector3::x() * 1.57, Point3::new(1.0, 2.0, 1.0));\n",
    "m.append_scaling_mut(2.0);\n",
    "\n",
    "let point1             = Point3::new(2.0, 3.0, 4.0);\n",
    "let homogeneous_point2 = Vector4::new(2.0, 3.0, 4.0, 1.0);\n",
    "\n",
    "// First option: use the dedicated `.transform_point(...)` method.\n",
    "let transformed_point1 = m.transform_point(&point1);\n",
    "// Second option: use the homogeneous coordinates of the point.\n",
    "let transformed_homogeneous_point2 = m * homogeneous_point2;\n",
    "\n",
    "// Recover the 3D point from its 4D homogeneous coordinates.\n",
    "let transformed_point2 = Point3::from_homogeneous(transformed_homogeneous_point2);\n",
    "\n",
    "// Check that transforming the 3D point with the `.transform_point` method is\n",
    "// indeed equivalent to multiplying its 4D homogeneous coordinates by the 4x4\n",
    "// matrix.\n",
    "assert_eq!(transformed_point1, transformed_point2.unwrap());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 构建MVP矩阵\n",
    "\n",
    "模型-视图-投影矩阵是三个转换的组合的共同名称：\n",
    "1. 模型变换将其方向和位置提供给3D场景中的对象。它对每个对象都是不同的。\n",
    "2. 将场景的任何点移动到摄影机的局部坐标的视图变换。它对于场景中的每个对象都是相同的，但对于每个相机都是不同的。\n",
    "3. 平移和拉伸场景的可显示部分的投影，使其适合双单位立方体（又名。归一化的设备坐标）。我们已经讨论过了。通常每个显示器只有一个投影。\n",
    "请注意，通常只构造视图-投影矩阵，并让图形卡联合收割机将其与着色器中的模型变换相结合。为了完整起见，我们的示例也将处理模型转换。\n",
    "\n",
    "模型和视图转换是直接等距的。因此，我们可以简单地使用专用的 Isometry3 类型。投影不是等距投影，需要使用原始 Matrix4 或专用投影类型（如 Perspective3 ）。\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "// Our object is translated along the x axis.\n",
    "let model = Isometry3::new(Vector3::x(), na::zero());\n",
    "\n",
    "// Our camera looks toward the point (1.0, 0.0, 0.0).\n",
    "// It is located at (0.0, 0.0, 1.0).\n",
    "let eye    = Point3::new(0.0, 0.0, 1.0);\n",
    "let target = Point3::new(1.0, 0.0, 0.0);\n",
    "let view   = Isometry3::look_at_rh(&eye, &target, &Vector3::y());\n",
    "\n",
    "// A perspective projection.\n",
    "let projection = Perspective3::new(16.0 / 9.0, 3.14 / 2.0, 1.0, 1000.0);\n",
    "\n",
    "// The combination of the model with the view is still an isometry.\n",
    "let model_view = view * model;\n",
    "\n",
    "// Convert everything to a `Matrix4` so that they can be combined.\n",
    "let mat_model_view = model_view.to_homogeneous();\n",
    "\n",
    "// Combine everything.\n",
    "let model_view_projection = projection.as_matrix() * mat_model_view;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let eye    = Point3::new(0.0, 0.0, 1.0);\n",
    "let target = Point3::new(1.0, 0.0, 0.0);\n",
    "let view   = Isometry3::look_at_rh(&eye, &target, &Vector3::y());\n",
    "\n",
    "let model      = Isometry3::new(Vector3::x(), na::zero());\n",
    "let projection = Perspective3::new(16.0 / 9.0, 3.14 / 2.0, 1.0, 1000.0);\n",
    "let model_view_projection = projection.unwrap() * (view * model).to_homogeneous();"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Screen-space到view-space \n",
    "投影矩阵任务是将可显示的3D对象拉伸和平移到双单位立方体中，即，它将点从视图坐标（相机局部坐标系）转换为标准化设备坐标（也称为clip-space）。然后，屏幕本身将包含从位于平面 \n",
    "z=-1\n",
    "z=−1 上的立方体表面可以看到的所有内容。因此，平行于z 轴的整条线（在剪辑空间中）将被映射到屏幕空间（显示设备的2D坐标系）上的单个点。下面显示了视图空间、标准化设备坐标和屏幕空间中的一个这样的行L 。有关计算机图形学中使用的不同坐标系的更多细节可以在那里找到。\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "现在观察屏幕空间中的每个点和剪辑空间中平行于 \n",
    "𝑧\n",
    "z 轴的每条线之间存在双射关系。此外，透视投影和正交投影都是双射的，并且将线映射到线。因此可以执行所谓的非投影，即，从屏幕空间中的2D点计算视图空间中相应的3D线。通常，这条线可以用于使用光线投射进行拾取。下一个示例在尺寸为 \n",
    "800×600 的屏幕上取一个点，并在视图空间中检索相应的行。它遵循三个步骤：\n",
    "1. 将屏幕空间中的点转换为剪辑空间中的两个点。一个将与 z=−1 位于近平面上，另一个将与 z=1 位于远平面上。\n",
    "2. 对两个点应用反向投影。\n",
    "3. 计算通过这两点的直线的参数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let projection   = Perspective3::new(800.0 / 600.0, 3.14 / 2.0, 1.0, 1000.0);\n",
    "let screen_point = Point2::new(10.0f32, 20.0);\n",
    "\n",
    "// Compute two points in clip-space.\n",
    "// \"ndc\" = normalized device coordinates.\n",
    "let near_ndc_point = Point3::new(screen_point.x / 800.0, screen_point.y / 600.0, -1.0);\n",
    "let far_ndc_point  = Point3::new(screen_point.x / 800.0, screen_point.y / 600.0,  1.0);\n",
    "\n",
    "// Unproject them to view-space.\n",
    "let near_view_point = projection.unproject_point(&near_ndc_point);\n",
    "let far_view_point  = projection.unproject_point(&far_ndc_point);\n",
    "\n",
    "// Compute the view-space line parameters.\n",
    "let line_location  = near_view_point;\n",
    "let line_direction = Unit::new_normalize(far_view_point - near_view_point);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 着色器的转换\n",
    "着色器不理解nalgebra定义的高级类型。因此，您通常需要将数据转换为指向连续浮点数数组的指针，其中组件在内存中以特定方式排列。使用原始矩阵和向量的 .as_slice() 方法，可以检索对连续数组的引用，该数组包含按列优先顺序的所有组件。请注意，对于不拥有其数据的矩阵（例如矩阵切片），此方法将不存在。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let v = Vector3::new(1.0f32, 0.0, 1.0);\n",
    "let p = Point3::new(1.0f32, 0.0, 1.0);\n",
    "let m = na::one::<Matrix3<f32>>();\n",
    "\n",
    "// Convert to arrays.\n",
    "let v_array = v.as_slice();\n",
    "let p_array = p.coords.as_slice();\n",
    "let m_array = m.as_slice();\n",
    "\n",
    "// Get data pointers.\n",
    "let v_pointer = v_array.as_ptr();\n",
    "let p_pointer = p_array.as_ptr();\n",
    "let m_pointer = m_array.as_ptr();\n",
    "\n",
    "/* Then pass the raw pointers to some graphics API. */"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rotation3 、 Similarity3 等更高级类型的转换无法直接转换为数组，因此您必须首先将它们转换为原始矩阵。 RotationMatrix3 和 RotationMatrix2 的底层3×3或4×4矩阵可以通过 .matrix() 方法直接检索。所有其他变换必须首先使用方法 .to_homogeneous() 转换为其齐次坐标表示。这将返回 Matrix2 或 Matrix3 ，然后可以将其重新解释为数组。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "let iso = Isometry3::new(na::zero(), Vector3::new(1.0f32, 0.0, 1.0));\n",
    "\n",
    "// Compute the homogeneous coordinates first.\n",
    "let iso_matrix  = iso.to_homogeneous();\n",
    "let iso_array   = iso_matrix.as_slice();\n",
    "let iso_pointer = iso_array.as_ptr();\n",
    "\n",
    "/* Then pass the raw pointer to some graphics API. */"
   ]
  }
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